Quantum isometry group of dual of finitely generated discrete groups - II

On sequences of finitely generated discrete groups

We consider sequences of discrete subgroups Γi = ρi(Γ) of a rank 1 Lie group G, with Γ finitely generated. We show that, for algebraically convergent sequences (Γi), unless Γi’s are (eventually) elementary or contain normal finite subgroups of arbitrarily high order, their algebraic limit is a discrete nonelementary subgroup of G. In the case of divergent sequences (Γi) we show that the resulti...

On finitely generated profinite groups, II: products in quasisimple groups

We prove two results. (1) There is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D ‘twisted commutators’ defined by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M = M(q) such that: if S is a finite quasisimple group with |S/Z(S)| > C, βj (j = 1, . . . ,M) ...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

Combinatorics of Finitely Generated Groups

of the Dissertation Combinatorics of Finitely Generated Groups